346 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT 
observed at the same temperature. In fact it will be seen that 
this result is verified very exactly, in all the cases in which the 
characteristic function eee) 
Plé 
On the other hand, if the inactive mass E is insufficient to 
saturate P, we have established in the same § 27 that the func- 
a(P+KE) 
P18 
the chemical groups formed in the mixed system according to 
the various doses of EK, its remaining constant under such cir- 
cumstances being an exceptional case. Thus, therefore, the 
different mixed systems which may be formed with P by suc- 
cessive additions of EK, should generally be effected with con- 
traction or expansion of volume; and this in fact takes place 
in the greater number of similar cases. This correspondence of 
variations, however, cannot be considered absolute; for experi- 
ence shows that very energetic combinations may take place 
even between gaseous substances without contraction or expan- 
sion of volume. Now, it will be seen that this last condition is 
found occasionally to coexist with variations, not only in the 
a(P + E) 
values, but in the sign of the characteristic function ThE 2 
is constant. 
tion should be generally variable, from the diversity of 
which undoubtedly attests the successive formation of chemical 
groups of a very different nature. 
39. To obtain the proofs here indicated, we must compose a 
formula expressing the density of a liquid system formed by the 
mixture, in whatever doses, of two other systems, which are 
supposed to mix without contraction or dilatation. Let 
é,, 8, be the proper densities of the two liquids, 
V,, V, the mixed volumes of each, 
P,, P, the respective weights of these volumes ; 
lastly, 
8, V, P the density, the volume, and the weight of the result- 
ing liquid. 
The condition of the mixture proposed will be 
Va +V,. 
Now the integral preservation of the composing weights, joined 
to the physical definition of the densities, gives 
P=P,+P, P=V8, P,=V,3,, P,=Ve% 
taking the expressions of the volumes V, V,, V, in the three 
